Wednesdays, 4 November–23 December 2026, 13:00–15:45 Moscow time. Online via Zoom, in English.

This course introduces neural networks as mathematical models and tools for scientific computing. It begins with a comparison of classical model-based approaches and neural network methods, followed by an introduction to basic neural network architectures.

The central part examines expressive power and generalization: what kinds of functions neural networks can approximate, and what theoretical results say about their performance on unseen data. The final part focuses on scientific applications through case studies and Python implementations. Across these topics, the course introduces the mathematical ideas and analytical tools used to study neural networks.

Prerequisites: Calculus, linear algebra, basic probability and statistics. Basic Python is recommended.

Course outline

• Part I — Introduction (2 weeks): Classical model-based methods and neural network approaches, with an introduction to basic neural network architectures.

• Part II — Expressive power and generalization (3 weeks): Why neural networks can approximate complex functions, and what is known about their ability to generalize to unseen data.

• Part III — Scientific computing (3 weeks): Recent scientific applications, explored through case studies and Python implementations.

The course concludes with a short report on a specific research topic.

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